Asynchronous Cooperative Networks: Performance Analysis and Code Design

Recently, cooperation was proposed as an alternative technique of multiple antennas (MIMO) systems in order to provide high spectral efficiency and spatial diversity improving the link reliability. The main idea is that multiple nodes in a network cooperate together to form a virtual antenna array. Cooperation permits, like the MIMO, to exploit space-time or cooperative diversity. However, unlike MIMO systems where the antennas are collocated, the antennas in cooperative systems are spatially distributed on different nodes. This new configuration can result in an asynchronism due to the difference in local oscillators and the different propagation and processing delays. The lack of perfect synchronization among the cooperative transmitting nodes destroys the required Space-Time Code (STC) signal structure at the receiver, leading to the reduction of the achievable diversity and thus deteriorates the code performance. Therefore, the STCs designed for MIMO systems are no longer valid for asynchronous cooperative communications. In the first part of this book, the effect of asynchronism on cooperative networks is studied from the point of view of outage probability, which is a pertinent performance metric. However, the exact evaluation of this probability for finite values of the Signal to Noise Ratio (SNR) is difficult most of the time. Therefore, we resort to the high SNR asymptotic approximation by deriving the Diversity Multiplexing Tradeoff (DMT) and the “outage gain”. Unlike the DMT, the outage gain can be used to compare the performance of two protocols having the same diversity gain or to optimize the power distribution among the transmitting nodes. The performances of a two cooperative transmitters network and two-relay networks with and without a direct link between the source and the destination are evaluated. It is shown that when no relative delay exists between cooperative nodes sending the same information, the diversity order of the network is equal to one, but with the presence of a delay, full transmit diversity is obtained. It is also proved that when the relative delay is sufficiently big (in the order of a few symbol periods), the outage gain becomes independent from the value of this delay. In the second part, appropriate Space Time Block Codes (STBC) are investigated for asynchronous cooperative networks. A general construction method based on optimal synchronous codes is designed to build delay tolerant codes for an arbitrary number of cooperative nodes and for bounded delay profiles. The new codes are referred to as “Bounded Delay Tolerant STBC”. These codes ensure optimal performances when the cooperative nodes are synchronous and a full diversity and optimal rate for an interval of delay profiles that varies with the code length. This design method consists of changing the order of the symbols to send by concatenating and permutating several code matrices and it is flexible with respect to the number of transmit and receive antennas, the signaling constellation and the transmission rate. However, because the length of the codewords can be large, the symbols detection at the receiver becomes more challenging and complex. Therefore, low complexity decoding methods providing acceptable performance are proposed to satisfy a certain performance-complexity tradeoff.